Numerous methods have been proposed for solving constrained optimization problems [1]}, [2]}. Compared to most of the existing literature on solving constrained optimization by either penalty methods, augmented Lagrangian methods, or sequential quadratic programming (SQP), we consider here a stochastic objective in Problem (REF ), whose exact function evaluation, gradient, and Hessian are inaccessible due to the expensive calculation of the expectation. However, their stochastic estimates are accessible by drawing samples from \({\mathcal {P}}\) . Recently, several algorithms built on stochastic SQP (StoSQP) have been proposed for solving (REF ). We point the reader to [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, and will review these related literature in Section REF . Although these works all showed global convergence for a variety of StoSQP schemes (with or without line search, with or without inequality constraints etc.), a “finer” understanding of StoSQP is missing.
